The arithmetic mean of x, y and z is 80, and that of x, y, z, u and v is 75, where u = (x + y)/2 and v = (y + z)/2. If x ≥ z, then the minimum possible value of x is
Explanation:
As the AM of x, y and z is 80, ⇒ x + y + z = 80 × 3 = 240 … (1)
As the AM of x, y, z, u and v is 75 ⇒ x + y + z + u + v = 75 × 5 = 375 … (2)
Subtracting equation (1) from (2), we get u + v = 135
∴ x+y2+y+z2=135
∴ x + 2y + z = 270 … (3)
Solving equations (1) and (3), we get ⇒ y = 30
∴ x + z = 210.
Now, since x ≥ z, the minimum value of x = 105.
Hence, 105.
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